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If this happened to someone in an undeveloped non-Western country that didn't have much contact with the rest of the world, or in a premodern society several centuries back, the character wouldn't have the ideas to think about his or her situation as a scientific problem. But a reasonably intelligent woman who grew up in the U.S. in the early 20th Century would at least know of the existence of a culture of science that could shed light on her condition.
This raises the question of whether a nonaging person encountering science after several centuries would have the abiltiy to absorb the implications of this relatively new and unintuitive way of thinking.
First option doesn't exist. The third world is well and truely aware that science is a thing. As for the second.. Writing someone who is old, but not impaired by decay is very, very difficult, due to lack of examples, but I think this might be less of a leap than it seems. Necessity will force mobility upon our protag, and contact with various cultures will immunize against believing received wisdom without proof. Going from there to "reality is the final arbiter" isn't much of a leap.
.. Now I am trying to think what applicable skills someone re... (read more)